Subgroups — C₂²×C₉×#41 #10593149

Order 576.

1335 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#41	C₂	1	24	yes	maximal, direct product factor
2	C₂²×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₄×C₉	C₂	1	3	yes	maximal, complemented
4	C₂³×C₄×C₉	C₂	1	3	yes	maximal, complemented
5	C₂²×C₃×#41	C₃	1	1	yes	maximal, characteristic
6	C₂⁴×C₉	C₂²	1	3	yes	—
7	C₉×#41	C₂²	1	64	yes	direct product factor
8	C₂×Q₈×C₉	C₂²	1	12	yes	complemented
9	C₂×D₄×C₉	C₂²	1	36	yes	complemented
10	C₂²×C₄×C₉	C₂²	1	3	yes	—
11	C₂²×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₉	C₂²	1	36	yes	complemented
13	C₂×C₃×#41	C₂×C₃	1	24	yes	—
14	C₂²×C₃×Q₈	C₂×C₃	1	1	yes	characteristic
15	C₂²×C₃×D₄	C₂×C₃	1	3	yes	—
16	C₂³×C₃×C₄	C₂×C₃	1	3	yes	—
17	C₂³×C₉	—	2	12	no	—
18	C₂³×C₉	C₂³	1	18	yes	—
19	C₂³×C₉	C₂³	1	1	yes	characteristic
20	Q₈×C₉	C₂³	1	16	yes	complemented
21	D₄×C₉	C₂³	1	48	yes	complemented
22	C₂×C₄×C₉	C₂³	1	18	yes	—
23	C₂×C₄×C₉	C₂³	1	6	yes	—
24	C₂×C₄×C₉	C₂³	1	48	yes	complemented
25	C₂²×#41	C₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₂⁴×C₃	C₂²×C₃	1	3	yes	—
27	C₃×#41	C₂²×C₃	1	64	yes	—
28	C₂×C₃×Q₈	C₂²×C₃	1	12	yes	—
29	C₂×C₃×D₄	C₂²×C₃	1	36	yes	—
30	C₂²×C₃×C₄	C₂²×C₃	1	3	yes	—
31	C₂²×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
32	C₂²×C₃×C₄	C₂²×C₃	1	36	yes	—
33	C₂²×C₉	—	2	36	no	—
34	C₂²×C₉	#41	1	4	yes	direct product factor
35	C₂²×C₉	C₂⁴	1	12	yes	—
36	C₂²×C₉	C₂⁴	1	3	yes	—
37	C₄×C₉	C₂⁴	1	4	yes	—
38	C₄×C₉	C₂⁴	1	12	yes	—
39	C₂×#41	C₂×C₉	1	24	yes	direct product factor
40	C₂²×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
41	C₂²×D₄	C₂×C₉	1	3	yes	complemented
42	C₂³×C₄	C₂×C₉	1	3	yes	complemented
43	C₂³×C₃	—	2	12	no	—
44	C₂³×C₃	C₂³×C₃	1	18	yes	—
45	C₂³×C₃	C₂³×C₃	1	1	yes	characteristic
46	C₃×Q₈	C₂³×C₃	1	16	yes	—
47	C₃×D₄	C₂³×C₃	1	48	yes	—
48	C₂×C₃×C₄	C₂³×C₃	1	6	yes	—
49	C₂×C₃×C₄	C₂³×C₃	1	18	yes	—
50	C₂×C₃×C₄	C₂³×C₃	1	48	yes	—
51	C₂×C₉	—	2	12	no	—
52	C₂×C₉	C₂×#41	1	6	yes	direct product factor
53	C₂×C₉	C₂⁵	1	1	yes	characteristic
54	C₂⁴	C₂²×C₉	1	3	yes	—
55	#41	C₂²×C₉	1	64	yes	direct product factor
56	C₂×Q₈	C₂²×C₉	1	12	yes	complemented
57	C₂×D₄	C₂²×C₉	1	36	yes	complemented
58	C₂²×C₄	C₂²×C₉	1	1	yes	characteristic
59	C₂²×C₄	C₂²×C₉	1	3	yes	—
60	C₂²×C₄	C₂²×C₉	1	36	yes	complemented
61	C₂²×C₃	—	2	36	no	—
62	C₂²×C₃	C₃×#41	1	4	yes	—
63	C₂²×C₃	C₂⁴×C₃	1	12	yes	—
64	C₂²×C₃	C₂⁴×C₃	1	3	yes	—
65	C₃×C₄	C₂⁴×C₃	1	4	yes	—
66	C₃×C₄	C₂⁴×C₃	1	12	yes	—
67	C₉	C₂²×#41	1	1	yes	characteristic, direct product factor, Sylow
68	C₂³	—	2	12	no	—
69	C₂³	C₂³×C₉	1	18	yes	—
70	C₂³	C₂³×C₉	1	1	yes	characteristic
71	Q₈	C₂³×C₉	1	16	yes	complemented
72	D₄	C₂³×C₉	1	48	yes	complemented
73	C₂×C₄	C₂³×C₉	1	6	yes	—
74	C₂×C₄	C₂³×C₉	1	18	yes	—
75	C₂×C₄	C₂³×C₉	1	48	yes	complemented
76	C₂×C₃	—	2	12	no	—
77	C₂×C₃	C₂×C₃×#41	1	6	yes	—
78	C₂×C₃	C₂⁵×C₃	1	1	yes	characteristic
79	C₂²	—	2	36	no	—
80	C₂²	C₉×#41	1	4	yes	direct product factor
81	C₂²	C₂⁴×C₉	1	12	yes	—
82	C₂²	C₂⁴×C₉	1	3	yes	—
83	C₄	C₂⁴×C₉	1	4	yes	—
84	C₄	C₂⁴×C₉	1	12	yes	—
85	C₃	C₂²×C₃×#41	1	1	yes	characteristic
86	C₂	—	2	12	no	—
87	C₂	C₂×C₉×#41	1	6	yes	direct product factor
88	C₂	C₂⁵×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₉	C₂²
commutator	C₂	C₂⁵×C₉
Frattini, cosocle	C₂×C₃	C₂⁵×C₃
socle	C₂³×C₃	C₂³×C₃
prime radical	C₂²×C₃×#41	C₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₉×#41	C₂	direct (N × H)
2. C₂²×Q₈×C₉	C₂	semidirect
3. C₂²×D₄×C₉	C₂	semidirect
4. C₂³×C₄×C₉	C₂	semidirect
7. C₉×#41	C₂²	direct (N × H)
8. C₂×Q₈×C₉	C₂²	semidirect
9. C₂×D₄×C₉	C₂²	semidirect
12. C₂²×C₄×C₉	C₂²	semidirect
20. Q₈×C₉	C₂³	semidirect
21. D₄×C₉	C₂³	semidirect
24. C₂×C₄×C₉	C₂³	semidirect
25. C₂²×#41	C₉	direct (N × H)
34. C₂²×C₉	#41	direct (N × H)
39. C₂×#41	C₂×C₉	direct (N × H)
40. C₂²×Q₈	C₂×C₉	semidirect
41. C₂²×D₄	C₂×C₉	semidirect
42. C₂³×C₄	C₂×C₉	semidirect
52. C₂×C₉	C₂×#41	direct (N × H)
55. #41	C₂²×C₉	direct (N × H)
56. C₂×Q₈	C₂²×C₉	semidirect
57. C₂×D₄	C₂²×C₉	semidirect
60. C₂²×C₄	C₂²×C₉	semidirect
67. C₉	C₂²×#41	direct (N × H)
71. Q₈	C₂³×C₉	semidirect
72. D₄	C₂³×C₉	semidirect
75. C₂×C₄	C₂³×C₉	semidirect
80. C₂²	C₉×#41	direct (N × H)
87. C₂	C₂×C₉×#41	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₉×#41	2
C₂²×Q₈×C₉	2
C₂²×D₄×C₉	2
C₂³×C₄×C₉	2
C₂²×C₃×#41	3

Subgroups — C22×C9×#41 #10593149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₉×#41 #10593149